Both presenters were in the running to replace Carson, with Leno eventually scoring the job and allegedly upsetting Letterman in the process.

Letterman spoke about his long rivalry with Leno on Oprah's Next Chapter and explained his mixed feelings about his former friend.

"I will say, and I'm happy to say, that I think he is the funniest guy I've ever known," he insisted to Oprah Winfrey. "Just flat out, if you go see him do his nightclub act, just the funniest, the smartest, a wonderful observationist and very appealing as a comic."

The Late Show host added: "The fact that he is also maybe the most insecure person I have ever known - I could never reconcile that."

Tensions between Leno and Letterman appear to have thawed in recent years, with the pair appearing with Oprah Winfrey in a Super Bowl commercial for The Late Show in 2010.

That Super Bowl advert was also originally supposed to include Conan O'Brien, who also has expressed ill-will towards Leno due to being replaced by the presenter on The Tonight Show three years ago. O'Brien ultimately declined to appear in the commercial.

Oprah's Next Chapter airs its Letterman interview on Sunday, January 6 at 9/8c on OWN.